Space density, denoted by ρ0, is a key parameter for modelling and constraining the Galactic CV population. Binary population synthesis studies in the literature have consistently predicted higher space densities for the Galactic CV population compared to observations, noting the seminal works of de Kool (1992) and Politano (1996) with predictions ρ0 '2×10−5 - 2.0×10−4 pc−3.
In attempts to reconcile the observable population with the intrinsic population, studies such as Gänsicke et al. (2009) have shown that there is potentially an abundance of intrinsically faint CVs close to the minimum orbital period which only adds to problem of collecting volume-limited samples (Pretorius, Knigge, and Kolb, 2007; Rau et al.,
5.7. The Galactic DNe population from the literature 115 2007). This poses a problem for direct comparison of our population size estimates the literature. Another unknown is the fractional composition of sub-populations, such as DNe, of the total Galactic CV population. Sub-populations also present according to different scale heights that stem from binary evolution within the galaxy and thus the Mróz et al. (2015) dataset probes the thin disk population (−10◦ < ` < 10◦) up to a maximum vertical distance of ∼ 1.5 kpc (Patterson, 1984). Higher space densities are expected for the long orbital-period type CVs at these low Galactic latitudes but the duration of the OGLE survey (∼ 10 years) means that it is insensitive to long orbital-period and low mass transfer rate (M˙) systems with long outburst recurrence times (Patterson, 1984; Pretorius, Knigge, and Kolb, 2007). The instrinsic faintness together with extinction and source confusion in the crowded field hinders representative sampling of the population. Recent efforts have been made to compile volume-limited samples and to map the distribution of the Galactic CV population
Figure 5.8: Figure 8 taken from Rau et al. (2007) showing predictions of the de- tectable population of quiescent DN according to the limiting R-band magnitude
of a given survey.
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Survey Limiting R- band Magnitude
Figure 5.8 taken from Rau et al. (2007) shows the expected number of quiescent DN systems that should be detectable brighter than a given limiting R-band magnitude.
According to the graph, for latitudes |b| < 10◦ and R < 21 magnitude, around 200 quiescent DN should be detectable, whilst only 20 are expected for R <18 magnitude.
If we correct for the colour difference between the I and R bands assuming a spec- tral classification of a K0→M8 type donor star then I −R ∼ −0.42 to −2.2 (colour corrections calculated from Zombeck (1990, P.69)). Thus, for a limiting I ∼21 magni- tude (i.e. that of the OGLE survey), this number increases to a range between ∼300 and ' 1700 detectable quiescent sources (Rau et al. (2007) assumes a space density ρ = 3×10−5 pc−3). This is in agreement with the detected sample size of 1059 DNe from the Mróz et al. (2015) dataset.
For I < 18.5 magnitude we might expect between 30 and 100 detectable quiescent sources according to Figure 5.8. If we define the quiescent state of each source as a ∆I ≤ 0.5 magnitude bin that it spends the majority of time over the course of the survey, then ∼ 152 DNe from the Mróz et al. (2015) sample are detectable in quiescence for I < 18.5 magnitude. This number is slightly larger than predictions in Rau et al. (2007). We note the unusually large fraction of the sample identified with outbursting magnitudes of less than 1 which could be argued to be misclassifications.
However, we will assume correct source classification for this discussion. Referring back to Table 5.3, the detected sample by the end of OGLE-IV is around 5 times larger (N = 783, I <18.5)) than those defined detectable at quiescence. The open population size estimates shown in Tables 5.4 and 5.5 range between 860.3±12.8 and 908.4±23.6. This implies that up to ∼17% of the population remains undetected in this flux-limited sample. A naive estimate of the space density of DN contained within the solid angle of |b|< 10◦,|`|< 10◦ out to a distance of 1 kpc (based on CV distances measured by Gaia-DR1 presented in Ramsay et al. (2017)) results in ρ ∼ 4×10−6 pc−3, neglecting scaleheight considerations. This estimate is an order of magnitude smaller than the assumed space density used for calculation in Rau et al. (2007). Although, our crude estimate is in agreement with the lower bound of 1.1+2.3−0.7 × 10−5 pc−3 obtained by Pretorius, Knigge, and Kolb (2007).
Unfortunately, the observational data for the CV population at Galactic latitudes of
|b| < 10◦ is very incomplete. A large CV sample (722 DN-type and 309 other-type) presented in Coppejans et al. (2016) from the CRTS focuses on latitudes above |b| >
15◦. Pretorius, Knigge, and Kolb (2007) uses the Palomar-Green (survey limited to latitudes |b| >30◦, Green et al. 1982) sample of CVs to simulate a potentially unseen population of DNe for magnitude limited cases of V < 20,16, and 14 magnitude. The
5.7. The Galactic DNe population from the literature 117 population size increases by a factor of more than 100 from the limit of V < 16 to V <20, most notably at the short orbital-periods, as they constitute the overwhelming majority of the total population. It is not simple to make meaningful comparisons with our results with regards to the intrinsic population located in the thin disk. Given the various caveats of the flux-limited (I <18.5 magnitude) sample, we present our results as lower bound estimates of the intrinsic thin disk population of DNe.
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